Below are listed temperaments of least TE complexity which result in a particular MOS shape, where "results in" is taken to mean that the POTE tuning has that shape.

7edo

5-limit

1L6s <<3 5 1|| porcupine 250/243
2L5s <<1 -3 -7|| mavila 135/128
3L4s <<2 1 -3|| dicot 25/24
4L3s <<5 6 -2|| sixix 3125/2916
5L2s <<1 4 4|| meantone 81/80
6L1s <<3 -2 -10|| enipucrop 1125/1024

7-limit patent

1L6s <<3 5 1 1 -7 -12|| hystrix {36/35, 160/147}
2L5s <<1 -3 -2 -7 -6 4|| {15/14, 64/63}
3L4s <<2 1 -4 -3 -12 -12|| dichotic {25/24, 64/63}
4L3s <<2 1 3 -3 -1 4|| dicot {15/14, 25/24}
5L2s <<1 4 -2 4 -6 -16|| dominant {36/35, 64/63}
6L1s <<3 -2 1 -10 -7 8|| {15/14, 256/245}

7d

1L6s <<3 5 2 1 -5 -9|| oxygen {21/20, 175/162}
2L5s <<1 -3 -4 -7 -9 -1|| pelogic {21/20, 135/128}
3L4s <<2 1 6 -3 4 11|| sharp {25/24, 28/27}
4L3s <<2 1 -1 -3 -7 -5|| flat {21/20, 25/24}
5L2s <<1 4 3 4 2 -4|| sharptone {21/20, 28/27}
6L1s <<4 2 5 -6 -3 6|| {25/24, 49/45}

8edo

5-limit

1L7s <<5 3 -7|| progression 3456/3125
2L6s <<2 6 5|| supersharp 800/729
3L5s <<7 9 -2|| sensi 78732/78125
4L4s <<4 4 -3|| diminished 648/625
5L3s <<1 -1 -4|| father 16/15
6L2s <<6 2 -11|| 18432/15625
7L1s <<3 5 1|| porcupine 250/243

7-limit 8d

1L7s <<5 3 7 -7 -3 8|| progression {36/35, 392/375}
2L6s <<2 -2 -2 -8 -9 1|| walid {16/15, 50/49}
3L5s <<1 -1 -5 -4 -11 -9|| pater {16/15, 126/125}
4L4s <<4 4 4 -3 -5 -2|| diminished {36/35, 50/49}
5L3s <<1 -1 3 -4 2 10|| father {16/15, 28/27}
6L2s <<6 2 2 -11 -14 -1|| {50/49, 192/175}
7L1s <<3 5 1 1 -7 -12|| hystrix {36/35, 160/147}

9edo

5-limit

1L8s <<4 -3 -14|| negri 16875/16384
2L7s <<1 6 -7|| avila 729/640
3L6s <<3 0 -7|| augmented 128/125
4L5s <<7 6 -7|| 93312/78125
5L4s <<2 3 0|| bug 27/25
6L3s <<3 9 7|| 19683/16000
7L2s <<1 -3 -7|| mavila 135/128
8L1s <<5 3 -7|| progression 3456/3125

7-limit

1L8s <<4 -3 2 -14 -8 13|| negri {49/48, 225/224}
2L7s <<1 6 5 7 5 -5|| {21/20, 243/224}
3L6s <<3 0 6 -7 1 14|| august {36/35, 128/125}
4L5s <<7 6 8 -7 -7 2|| {36/35, 686/625}
5L4s <<2 3 1 0 -4 -6|| beep {21/20, 27/25}
6L3s <<3 9 6 7 1 -11|| {21/20, 729/686}
7L2s <<1 -3 -4 -7 -9 -1|| pelogic {21/20, 135/128}
8L1s <<5 3 7 -7 -3 8|| progression {36/35, 392/375}

10edo

5-limit

1L9s <<4 7 2|| 2500/2187
2L8s <<2 -4 -11|| srutal 2048/2025
3L7s <<2 11 13|| 204800/177147
4L6s <<14 12 -13|| 6103515625/4353564672
5L5s <<0 5 8|| blackwood 256/243
6L4s <<6 8 -1|| 15625/13122
7L3s <<2 1 -3|| dicot 25/24
8L2s <<2 6 5|| supersharp 800/729
9L1s <<4 -3 -14|| negri 16875/16384

7-limit

1L9s <<4 7 2 2 -8 -15|| {49/48, 175/162}
2L8s <<2 -4 -4 -11 -12 2|| pajara {50/49, 64/63}
3L7s <<2 11 6 13 4 -17|| {28/27, 2401/2400}
4L6s <<4 2 2 -6 -8 -1|| decimal {25/24, 49/48}
5L5s <<0 5 0 8 0 -14|| blacksmith {28/27, 49/48}
6L4s <<6 8 8 -1 -4 -4|| {50/49, 175/162}
7L3s <<2 1 6 -3 4 11|| sharp {25/24, 28/27}
8L2s <<2 6 6 5 4 -3|| octokaidecal {28/27, 50/49}
9L1s <<4 -3 2 -14 -8 13|| negri {49/48, 225/224}

11-limit

1L9s <<4 7 2 5 2 -8 -6 -15 -13 7|| {35/33, 49/48, 55/54}
2L8s <<2 -4 6 0 -11 4 -7 25 14 -21|| {28/27, 35/33, 128/121}
3L7s <<2 1 -4 -5 -3 -12 -15 -12 -15 0|| dichosis {25/24, 35/33, 64/63}
4l6s <<4 2 2 0 -6 -8 -14 -1 -7 -7|| decibel {25/24, 35/33, 49/48}
5L5s <<0 5 0 5 8 0 8 -14 -6 14|| ferrum {28/27, 35/33, 49/48}
6L4s <<6 8 8 10 -1 -4 -5 -4 -5 0|| {35/33, 50/49, 55/54}
7L3s <<2 1 6 5 -3 4 1 11 8 -7|| sharp {25/24, 28/27, 35/33}
8L2s <<2 6 6 10 5 4 9 -3 2 7|| {28/27, 35/33, 50/49}
9L1s <<4 -3 2 5 -14 -8 -6 13 22 7|| negri {45/44, 49/48, 56/55}

11edo

5-limit 11b

1L10s <<7 4 -10|| 82944/78125
2L9s <<3 8 6|| 8000/6561
3L8s <<10 1 -22|| 12582912/9765625
4L7s <<6 5 -6|| hanson 15625/15552
5L6s <<2 9 10|| 25600/19683
6L5s <<9 2 -18|| 2359296/1953125
7L4s <<5 6 -2|| sixix 3125/2916
8L3s <<1 10 14|| 81920/59049
9L2s <<8 3 -14|| 442368/390625
10L1s <<4 7 2|| 2500/2187

5-limit 11c

1L10s <<5 8 1|| ripple 6561/6250
2L9s <<1 -5 -10|| 1215/1024
3L8s <<4 13 11|| 1594323/1280000
4L7s <<9 10 -5|| 1953125/1889568
5L6s <<3 7 4|| laconic 2187/2000
6L5s <<8 15 5|| 14348907/12500000
7L4s <<13 12 -11|| 1220703125/1088391168
8L3s <<7 9 -2|| sensi 78732/78125
9L2s <<1 6 7|| avila 729/640
10L1s <<5 -14 -33|| 14946778125/8589934592